The actual (left) and cumulative (right) distribution of points obtained by the participants are
shown for different marking schemes. The schemes differ in the number of points attributed to
1, 2, 3 or 4 correct answers per question (see legend) with the actual marking scheme used
in the IBO 2013 shown in purple, the only originally proposed by the organizers in blue and
the harshest and mildest marking schemes possible in red and green, respectively. The points
were standardized such that 1 corresponds to the maximum number of points that could be
obtained in the exam (92, regardless of marking scheme).

Total Scores and Difficulty

In line with the results of previous IBOs, the theoretical exam proved to be rather difficult,
regardless of the marking scheme. Under the marking scheme used for the IBO 2013, the
median relative score was 0.58 (standardized such that 1 corresponds the maximum attainable
number of points). While one student obtained a score (0.27) slightly below the relative score
expected for students guessing every item (0.29), the highest score obtained was only 0.8152.
For comparison, an ideal exam would show a median value of about 0.64 (in the middle of
0.29 and 1) with the individual scores distributed uniformly between 0.29 and 1.

The overall difficulty of the exam is confirmed when analyzing the distribution of correct
answers given by the participants for each question individually ( FIGURE 6 .14). While we
found the questions to show varying degrees of difficulty, there is an apparent lack of easy
questions with very few questions showing an average above 0.8. It thus suggests that a more
reliable ranking would be obtained by using questions that were slightly easier on average.
On a bright side, even the most difficult questions were still solved better than expected if
students were only guessing.